#16477: implement Dirichlet series
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: number theory | Resolution:
Keywords: moebius, zeta, | Merged in:
sigma, euler_phi, euler | Reviewers:
Authors: Jonathan Hanke, | Work issues: use pari, g.f. input
Ralf Stephan | Commit:
Report Upstream: N/A | 5698ef17c2be57ebe3826737cdba43f12c6bb8d6
Branch: u/rws/16477-1 | Stopgaps:
Dependencies: |
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Comment (by jj):
Replying to [comment:44 rws]:
> I vaguely remember having had a look at some time but now I see you're
right.
Note that L-function / L-series usual refer to functions / series
satisfying
some very specific (more restrictive) set of axioms (AC/FE/etc) - in
contrast
to Dirichlet series or abstract Dirichlet series. So there is definitely
some
justification for introducing a new class (at least if it supports exact
representation).
Also if I remember correctly the L-function is not an exact representation
but
also restricted by precision. What I would like to see is support for
exact
abstract Dirichlet series, e.g. by using symbolic coefficient functions or
by using exact generating series in terms of rational functions.
If they are not implemented in an exact way I am curious about the
background:
How / in what context will they be used? Why is a new class required?
In any case I agree that Dirichlet series don't belong to sage.modular.
Best
Jonas
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Ticket URL: <http://trac.sagemath.org/ticket/16477#comment:45>
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